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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

On a certain pair of measures on $ \ell_p$


Author: E. A. Riss
Translated by: the author
Original publication: Algebra i Analiz, tom 25 (2013), nomer 1.
Journal: St. Petersburg Math. J. 25 (2014), 105-115
MSC (2010): Primary 28C20
DOI: https://doi.org/10.1090/S1061-0022-2013-01281-7
Published electronically: November 20, 2013
MathSciNet review: 3113430
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Abstract | References | Similar Articles | Additional Information

Abstract: A pair of finite Borel measures $ \mu $ and $ \nu $ on $ \ell _p$, $ 1\le p< \infty $, $ \mu \ne \nu $, is constructed so that the identity $ \mu (B(x,r))=\nu (B(x,r))$ is fulfilled for all balls $ B(x,r)$ with centers $ x \in \ell _p$ and radii $ r<R(x)$, where $ R(x)>0$ for a.e. $ x$.


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Additional Information

E. A. Riss
Affiliation: Hertzen Russia State Pedagogical University, Moika 48, St. Petersburg 191186, Russia
Email: e.riss@bk.ru

DOI: https://doi.org/10.1090/S1061-0022-2013-01281-7
Keywords: Measures on Banach spaces, small ball problem
Received by editor(s): May 4, 2012
Published electronically: November 20, 2013
Article copyright: © Copyright 2013 American Mathematical Society

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